ABSTRACT
Optimization has found widespread applications in data analysis during the past few years. Prominent examples include a variety of stochastic optimization models for machine learning (e.g., regression, classification, dictionary learning), and deterministic optimization models for inverse problems (e.g., compressed sensing, image reconstruction and matrix completion). Although being very encompassing, such optimization models from data analysis are often challenging to solve, mainly due to their high problem dimensionality, inherent data uncertainty, pervasive structure ambiguity, along with the frequent need to solve them in real time. In this talk, I will survey some recent advances to tackle the aforementioned big-data challenges in optimization. In particular, I will highlight: i) novel stochastic optimization methods that can handle data uncertainty in an optimal manner, based on our work on stochastic approximation; and ii) new deterministic optimization methods that converge faster and require little structural information, based on our work on level methods. I will provide showcases for the effectiveness of these techniques in machine learning and biomedical imaging.